Method for quantitative analysis of cavity zone of the top of concrete-filled steel tube

A method for quantitatively determining a height of a cavity in a steel tube containing concrete, comprising:

• determining an inner radius of the steel tube, the steel tube having a wall;
• determining a thickness of the wall of the steel tube;
• determining a propagation speed of an ultrasonic wave in each of (i) the steel tube and (ii) the concrete;
• using ultrasonic sensors on an outer surface of the wall of the steel tube containing the concrete, at a top of the steel tube and at a bottom of the steel tube, determining a propagation time of the ultrasonic wave propagating between the top and the bottom of the steel tube containing the concrete;
• and
• calculating the height of the cavity according to:
• t
• =
• (
• x
• 1
• +
• d
• 2
• +
• 2
• ⁢
• x
• 2
• (
• d
• +
• r
• )
• v
• s
• +
• 4
• ⁢
• r
• 2
• +
• d
• 2
• +
• 4
• ⁢
• r
• ⁢
• d
• -
• 2
• ⁢
• r
• ⁢
• h
• -
• 2
• ⁢
• h
• ⁢
• d
• -
• d
• 2
• +
• 2
• ⁢
• x
• 2
• (
• d
• +
• r
• )
• v
• c
• )
• wherein t is the propagation time of the ultrasonic wave in seconds;
• r is the inner radius of the steel tube in meters;
• d is the thickness of the wall of the steel tube in meters;
• h is the height of the cavity in the steel tube in meters;
• vs and vc are the propagation speeds of the ultrasonic wave in the steel tube and in the concrete, respectively, in m/s;
• and x1 and x2 are both calculation variables having values dependent on h.